Aggregate Nominal Wage Adjustments: New Evidence from Administrative Payroll Data

Transcription

1 Aggregate Nominal Wage Adjustments: New Evidence from Administrative Payroll Data John Grigsby Erik Hurst Ahu Yildirmaz Preliminary and Evolving July 2, 2018 Abstract Using administrative payroll data from the largest U.S. payroll processing company, we document a series of new facts about the extent of nominal wage adjustments in the U.S.. First, we document that nominal wage cuts are exceedingly rare for job-stayers. Over the pooled period, only 2% of workers who remain in a continuous employment relationships receive a nominal wage cut during a given year. Second, nominal wages are much more flexible (both up and down) for job changers. Aggregating job changers and job stayers shows that approximately 10% of workers receive a wage cut during a year. Third, the extent of wage rigidity is state dependent. Nominal wage adjustments are lower during recessions, in regions that suffered larger house price declines, and for firms that shed large amounts of workers. Moreover, nominal wage cuts are substantially higher during recessions. During the Great Recession, nearly 12 percent of workers received a nominal wage cut. Wage declines during the recession were particularly concentrated in areas with large house price declines and in shrinking firms. We end by discussing how measurement error in household level data and missing measures of hours in firm level data substantially bias existing measures of nominal wage rigidity. We thank Mark Aguiar, Steve Davis, John Haltiwanger, Alan Krueger, Marianna Kudlyak, John Shea, Rob Shimer, and Joe Vavra as well as seminar participants at the 2018 American Economic Association meetings, Chicago, the European Central Bank, Maryland, the San Francisco Federal Reserve, and USC for helpful comments. Authors contact information: jgrigsby@uchicago.edu, erik.hurst@chicagobooth.edu. and Ahu.Yildirmaz@ADP.com.

2 1 Introduction The degree to which wages are flexible determines the extent to which economic shocks generate macroeconomic fluctuations in employment and earnings. In addition, modern New Keynesian models often show that the nominal wage rigidities dictate the aggregate response of real variables to monetary policy shocks. However, compared to the literature on price changes, there is only a relatively small literature which uses micro data to measure the extent to which nominal wages adjust. That different questions necessitate different measures of rigidity complicates this measurement exercise. Studies seeking to quantify the effect of downward nominal wage rigidity on employment flows will be concerned with within-job flexibility for job stayers, while studies of the aggregate response to monetary shocks require an aggregate measure of rigidity which accounts for the wage movements of both job-stayers and job-changers. Furthermore, most micro data sets are not well suited to measure nominal wage changes. Household surveys often define the nominal wage by dividing self-reported earnings by self-reported hours. Any measurement error in either earnings, hours worked, or the self-reported hourly wages can result in a substantial upward bias in the volatility of individual level wage changes. Administrative datasets, on the other hand, have high quality panel data on quarterly or annual earnings but usually do not have measures of individual hours worked. 1 The lack of data on hours worked makes administrative datasets less than ideal when it comes to studying nominal wage fluctuations. In this paper, we use administrative data from ADP one of the world s largest payroll processing companies to document a series of facts about aggregate nominal wage adjustments for millions of U.S. workers during the last decade. Hundreds of thousands of firms per year contract with ADP to administer a variety human resource and payroll activities. Most of ADP s clients use their payroll processing services, with ADP currently processing payroll checks for roughly 20 million workers each year, one-seventh of the U.S. workforce. We have access to data from 2008 through For workers paid hourly, the data records administrative measures of their hourly wage. For salaried workers, we observe administrative measures of the employees contracted earnings per pay period. Some salaried workers are paid weekly while others are paid bi-weekly or monthly. The administrative data records their contractually obligated per-period pay rate. We also have detailed administrative data on a workers gross monthly earnings (i.e., the sum of their monthly paychecks). 1 When individual hours worked are collected, they are often reported not by the individual but instead by a payroll administrator. For example, Washington is one state that uses hours worked in the prior year to determine UI eligibility. As we highlight later in the paper, such administrative reports of hours worked for salaried workers are likely measured with sufficient error to lead to overstated nominal wage adjustments if the measure of the nominal wage is earnings per hour. 1

3 Note, that monthly gross earnings will differ from a worker s per-period contract rate. A worker s monthly earnings will account for hours worked during the month (for hourly workers) and the number of pay periods per month (for salaried workers). Additionally, during the month the worker could receive overtime compensation, tips, commissions, meal and travel reimbursements, pay advances, signing bonuses, severance payments, cashed-out vacation time, quarterly performance pay, and annual bonuses which is accrued above and beyond a worker s base pay. This paper makes three principal contributions. First, the richness of the ADP data allows us to present new facts on the forms of compensation for American workers, and find that the overwhelming majority of earnings are in base pay. We refer to base pay as the part of earnings directly resulting from the worker s per-period pay rate. We then define a worker s nominal wage as their per-period contract rate. Second, we use our data to present several key facts about nominal wage adjustments for job-stayers, testing the common assumptions of Calvo, time dependent, and state dependent wage setting. We present substantial evidence for both state and time dependence in wage setting for jobstayers. 2 Finally, we measure the extent of aggregate nominal wage rigidity in the economy for the economy as a whole combining data on both job-stayers and job-changers. Given the fact that the nominal wages of job-changers are quite flexible, We find substantially more nominal rigidity for job-stayers than for the economy as a whole. We begin the paper documenting how much worker compensation comes from different sources. For most workers, essentially all of their monthly earnings is attributed to their contractually obligated base pay. Focusing only on workers who are continuously employed with the same firm for a 12 month calendar period, the median hourly worker receives 97% of their annual earnings in base pay, while the equivalent number for salaried workers is 95%. Much of the additional income comes in the form of year end bonuses. We estimate that about one-out-of-five hourly workers and one-out-of-three salaried workers receive an annual bonus of at least 1 percent of their gross annual earnings. The average bonus size for hourly and salaried is, respectively about $1,600 and $5,400 per year. Given that the bulk of annual compensation for most workers is in base pay and annual bonuses, we focus our attention in the rest of the paper examining how base pay and bonus compensation evolves. To measure aggregate nominal wage adjustments, we explore how nominal wages (as measured by per-period administrative contract rate) evolves for those workers who remain employed within the same firm. We refer to such workers as job-stayers. We then separately explore how nominal wages evolve for those workers who switch jobs. ADP s large 2 Bils and Klenow (1995) and Nakamura and Steinsson (2008) similarly present numerous facts about the nature of output price setting. 2

4 coverage of the US workforce allows us to observe workers migrating from one ADP firm to another ADP firm within a relatively short time period. Using data from Census s Job-to-Job flows which measures the amount of job-stayers relative to job-changers in the economy as a whole, we can aggregate our data to make a measure aggregate nominal wage adjustments. We complement our analysis by exploring how bonuses evolve for a given worker over time. We begin our analysis by describing key facts of the wage setting process for job-stayers. Roughly 20 percent of job-stayers receive a nominal wage change over a quarter and about two-thirds of job-stayers receive a wage change during a year pooling over our full sample period. However, small wage changes of less than 2% are rare, consistent with menu cost models of wage setting. Unlike other studies in the literature, we find that nominal wage cuts for job-stayers are exceedingly rare. For our sample of job-stayers during the period, only 0.9 percent of workers received a nominal wage cut during a given quarter and only 2.4 percent received a nominal wage cut during a given year. Essentially all wage changes within a given employment relationship are wage increases. This strong downward rigidity on the job may be an important factor for the large employment fluctuations observed during the Great Recession. Wage adjustment patterns vary systematically by both firm size and industry. Smaller firms are much less likely to adjust wages than larger firms. Additionally, the frequency of wage adjustment is higher in the manufacturing, FIRE and services industries and lower in construction, retail trade and wholesale trade. These differences persist even conditional on a vector of individual and firm level controls. We then provide evidence supporting the importance of time dependent wage setting, reflecting a model of Taylor (1980) staggered wage contracts at the individual level. In a sample of job-stayers, wage adjustments occur primarily at 12 month intervals. There is a small and constant probability of wage changes between 1 and 10 months and between 14 and 22 months suggesting that at the individual level, some wage changes occur at frequencies other than a year. The nature of these wage changes are different in that they are much larger than the wage changes that occur at annual frequencies. While, for the most part, workers receive a wage change every 12 months, the wage changes at the aggregate level are mostly smoothed out across individuals. Exploring the seasonality in wage changes, we find that wage changes are more common in January, April and July than in other months during the year. However, aggregating to quarters, the fraction of wage changes is roughly constant across quarters. We next turn to the measurement of wage rigidity for the aggregate economy. Given the extensive nature of the ADP data, we can also measure wage changes for individuals who transition across firms. This is only possible for workers that transition from one firm who 3

5 uses ADP payroll services to another firm that uses ADP payroll services. Given our large sample sizes, we have many workers who transition across ADP firms. Almost all workers that transition across jobs experience a nominal wage change. Given that job switchers are a non-trivial share of the economy, we create a broader measure of nominal wage flexibility pooling together both job stayers and job changers. Doing so, we find that roughly 26 percent experience a wage change during a given quarter and 73 percent experience a wage change during a given year. Including both the job stayers and job changers, roughly 10 percent of workers experience a nominal wage decline with essentially all of the declines being driven by job changers, 38 percent of whom realize a wage decline during our sample. That the aggregate economy, including job switchers, exhibits a substantially higher degree of flexibility than the sample of job-stayers is a key insight of this paper. Models seeking to understand the muted fluctuations in mean nominal wages over the cycle must reckon with this finding that aggregate wages are relatively flexible on the downside given the presence of job-changers. In addition, models without realistic job search components should be cautious about using wage rigidity estimates from job-stayer samples, as is standard in the literature, for doing so will result in overstating the degree of rigidity in the economy as a whole. After documenting the difference between aggregate and individual wage rigidity, we examine the extent to which wages are able to adjust to shocks. We provide strong evidence that wage setting behavior is state dependent. Even though nominal wage cuts are very rare for job-stayers over our entire sample period, roughly 6.6 percent of salaried workers and 2.8 percent of hourly workers received nominal wage cuts during the Great Recession. Although the share of job switchers, who are much more likely to see wage declines, fell during the recession, the aggregate propensity to receive a wage decline year-over-year was 11.8% during the recession, compared with 9.7% during the recovery. Indeed, the mean wage growth for a worker rose from 2.7% during the recession to 5.2% during the recovery, though this change was mostly driven by the decline in the share of workers receiving cuts: the conditional mean size of wage increases and decreases did not vary much over the cycle. Moreover, we show that nominal wage cuts were much more likely in parts of the country that received large housing price declines. This suggests that any model with a constant fraction of wage adjustments (either in general or with respect to downward adjustment) will fail to match the wage setting patterns over a business cycle. The fact that wages adjust more on the downside during recessions serves to strengthen the puzzle of increased unemployment at business cycle frequencies. Furthermore, the presence of this state dependence in wage adjustment suggests that wages are indeed more downwardly flexible than much of the literature has assumed. To complement our macro business cycle results, we explore cross-firm variation in wage setting in response to underlying firm level shocks. We document that firms with declining 4

6 employment were much more likely to reduce the nominal wages of their workers relative to either firms with constant or increasing employment during the recession. Following the recession, however, this pattern became much more muted, as growing firms and shrinking firms were equally unlikely to cut wages. Instead, shrinking firms during the recovery were much less likely than growing firms to increase workers wages. However, even firms with sharply declining employment raise the wages of many of their employees, both during and after the recession. The interaction between idiosyncratic and aggregate conditions for determining on-the-job wage adjustment patterns suggests that the value of workers outside options are important for realized wage rigidity, and again urges considerations of models with state dependent wage adjustment. We end the paper discussing how our results fit into the existing literature on nominal wage adjustments. In doing so, we highlight the importance of using administrative payroll data to measure the extent of nominal wage adjustments among workers. To help illustrate the benefits of administrative payroll data, we create two additional measures of nominal wage adjustments throwing away some of the strength of our data. First, we measure changes in quarterly earnings for a given worker who remains with a given firm. Then we measure quarterly earnings per hour. Both of these approaches use our administrative data on earnings instead of our administrative data on per-period contract rates. The latter of these new measures adjusts earnings by administrative measures of hours worked. We show that both of these measures lead to substantially higher amounts of perceived wage adjustment for workers who remain on the same job. Some of this is due to the fact that earnings includes lots of other forms of compensation like overtime payments, severance payments, commissions, tips, and annual bonuses. However, another important reason is that administrative measures of hours worked for salaried works are measured with substantial error. To drive this point home, we compute changes in quarterly base earnings per hour for both hourly and salaried workers. By focusing on only base earnings per hour allows us to highlight explicitly the measurement error in hours within administrative datasets (including APD). For hourly workers, changes in quarterly base earnings per hour mimic nearly identically changes in per-period contract rates. However, for salaried workers, the standard deviation in changes in quarterly base earnings per hour far exceeds the standard deviation in changes in per-per contract rates. The only reason for this is the volatility in hours worked per quarter for salaried workers. Given that it is nearly impossible for firms to measure with any degree of accuracy hours worked for salaried workers, it is difficult to interpret with any confidence changes in quarterly earnings per hour as a measure of nominal wage adjustments for salaried workers. Collectively, these results highlight the importance of using administrative payroll 5

7 data to accurately measure nominal wage adjustments. Overall, our results suggest important differences between aggregate and on-the-job wage rigidity. Removing the measurement error that plagues household surveys and administrative hours measures reduces measured nominal wage rigidity for job-stayers substantially, and reveals substantial downward on-the-job rigidity. However, since job changers have much more flexible wages, aggregate wages are much more flexible. Furthermore, we show complementary evidence supporting state dependence in wage setting, urging further consideration of menu cost models of wage adjustment. While there is no doubt that there is some short run stickiness, particularly on the downside, most workers do receive nominal wage adjustments within a year. The paper proceeds as follows. Section 2 describes the ADP data in detail, and provides summary statistics to benchmark the data to existing data sources. Section 3 describes the allocation of worker compensation across base pay and bonuses. Section 4 presents key facts about wage adjustment for job-stayers, such as the distribution of wage changes, patterns by industry, and evidence of time dependence in wage setting. Section 5 present wage change statistics for job changers, and presents our measures of aggregate nominal wage adjustments. Sections 6 and 7 present evidence of state dependence at the aggregate and regional levels, respectively. Finally Section 8 compares our measures of rigidity to those found in the literature. Section 9 concludes. 2 Data 2.1 Overview of ADP Data We use administrative individual panel data provided by the ADP Corporation. ADP is a large, international provider of human resources services including payroll processing, benefits management, tax services, and compliance. ADP has over 650,000 clients worldwide, and currently covers payroll for over 20 million individual workers in the United States per month. The data to which we have access starts in May 2008 and extends through December During that period, we observe payroll information for approximately 12% of the American workforce. The data contain monthly aggregates of individual paycheck information, as well as all relevant pieces of information needed for human resources management. Crucially, we observe, without measurement error, the statutory per-period payment rate for all employees. For hourly workers, this payment rate is simply the worker s hourly wage, while for salaried workers, this constitutes the pay that the worker is contractually obligated to receive each 6

8 pay period (weekly, bi-weekly, or monthly). For much of our analysis, we consider hourly and salaried workers separately. Given the data is aggregated to the monthly level, the per period payment rate is measured as of the last pay period of the month. In addition to the administrative wage information, the data contain all other information that would appear on the worker s paycheck, such as the worker s gross earnings per pay period, taxes paid, and any taxable benefits provided by the firm. Additionally, the data contain other payroll information including whether the worker is paid hourly, the frequency at which the worker is paid and the number of hours worked during the month. For hourly workers, this is the exact number of hours worked. For salaried workers, these data are provided by the firm s HR administrator and is often set to 40 hours. We also observe various additional worker characteristics including their zip code of residence, sex, and age, as well as details about the job, such as the start date of employment (and thus worker tenure), firm size, and industry. Selection into the ADP data is at the firm level. As a result, given unique firm identifiers, we can measure wage distributions within and across firms over time. 3 Finally, the presence of consistently-defined worker identifiers permits the careful study of individual worker dynamics across firms. The one caveat is that we are only able to track workers if they move to another ADP-covered firm. However, given our sample size, movements from one ADP firm to another ADP firm are quite common. We make two major sample restrictions for our analysis. First, we restrict ourselves to workers aged 21 through 60 years old. This restriction focuses our analysis on prime age workers. Second, we only make use of data from ADP s Autopay payment product, which is marketed principally towards firms with over 50 employees. Autopay is ADP s primary payroll processing product. 4 Therefore, our data is restricted to include only firms with more than 50 employees. 5 The full dataset that we have access to includes over 50 million unique individuals and over 141 thousand firms. To reduce computational burden, we create two random subsamples of the full data. The first chooses one million unique employees, and follows them through their entire tenure in the sample. This is the primary dataset for analysis. However, this dataset is ill-suited to study questions at the firm level; we therefore construct a second 3 Strictly speaking, our definition of a firm is an ADP-provided client code. This will usually be an autonomous firm, rather than any individual establishment. One possible exception to this rule arises if particularly large conglomerates have multiple subsidiaries, all of which separately hire ADP to handle their payroll. In this case, each subsidiary would count as a separate ADP client. 4 ADP does have a separate product called Run marketed to smaller firms. We have access to this dataset but only starting in July In the online appendix, we document that many of the main patterns documented for the smaller firms in our primary sample match the patterns for smaller firms in the Run sample for overlapping time periods. 5 There are a few workers in the Autopay database that work at firms with less than 50 employees. We exclude these few workers from our analysis. 7

9 subsample of three thousand unique ADP clients, drawing all workers from those firms in the process. The random employee-level and firm-level subsamples remain large, with roughly 25 million and 68 million unique employee-month observations, respectively. 2.2 Representativeness of ADP Data Table 1 highlights the firm size distribution for employees in our employee sample (column 1) and employees in our firm sample (column 2). For the results in this table, we pool our data together over the entire period. The table also shows the number of employees and the number of firms in each of our samples. By design, we randomly drew 1 million employees for our employee sample and 3,000 firms for our firm sample. Our employee sample includes roughly 91,500 distinct firms while our firm sample includes roughly 3.3 million distinct employees. The number of actual observations is much larger for each sample because we observe employees for multiple months. For our employee sample, we track employees across all months between 2008 and 2016 that they are employed at any ADP firm. For our firm sample, we track all employees in that firm across all months that they remain employed at that firm. For comparison, column 3 of Table 1 includes data from the U.S. Census s Business Dynamics Statistics (BDS) over the same time period. As discussed above, we have access over the entire period for ADP s product that is marketed to firms with more than 50 employees. Given this, we have no employees in our base samples that work at firms with less than 50 employees. According to BDS data, 28% of employment is in firms with less than 50 employees. For comparison with our data, column 3 shows the share of employment in firms of differing size relative to employment in all firms with at least 50 employees. As seen from the table, the ADP also slightly under-represents very large employees (those with at least 50 employees). The reason for this is that very large firms tend to have their own human resource department that processes their payroll. Additionally, large firms may be more likely to split into multiple distinct ADP clients. Despite this, ADP still has a large number of employees working in firms with over 5,000 employees. We also explore how the industry distribution of the ADP sample compares to the industry distribution in the BDS. The ADP sample has a slight over-representation amongst the manufacturing and broad service sectors, and a complementary underweight in retail trade, construction, and agriculture. To account for the concern that the data do not perfectly represent the universe of all U.S. firms with at least 50 employees, all subsequent analyses in this paper have been weighted so as to match the BDS s firm size by industry mix of employment shares for firms with greater 8

10 Table 1: Firm Size Distribution in ADP Samples and the BDS, Pooled Data Pooled ADP Employee Sample ADP Firm Sample BDS Data Number of Employees 1,000,000 3,296,701. Number of Firms 91,577 3,000. Number of Observations 24,831,244 68,267,166. % Firm Size: % Firm Size: % Firm Size: % Firm Size: Note: than 50 employees. We compute our weights for each year between 2008 and By reweighting the data, we control for sample selection along these key observable dimensions. Although there may yet remain selection into the sample along unobservable dimensions (e.g., firms with high cash flow are more likely to hire ADP), we consider these potential selection issues to be small once controlling for firm size and industrial mix. 6 Table 2 shows some additional summary statistics for our employee sample pooling across all years (column 1) and for selected individual years (columns 2-4). In particular, we show statistics for 2008 (our first year of data), 2012 (a middle year of data), and 2016 (our last year of data). As discussed in the Online Appendix, the age, sex, and tenure distributions in our ADP sample matches well the age, sex, and tenure distributions of workers in nationally representative surveys such as the Current Population Survey (CPS). About one-fifth of our sample is paid weekly while three-quarters is paid bi-weekly. Less than five percent are paid monthly. For our sample, roughly 64 percent are paid hourly with the remaining 36 percent being classified as salaried workers. According to data from the CPS monthly supplements, only 57 percent of employed workers in the U.S. between the ages of 21 and 60 report being paid hourly during this time period. The difference between the CPS and ADP data may arise as the distinction between hourly and salaried workers is sometimes unclear within the ADP dataset. Some hourly workers in the ADP data are automatically entered as having worked 40 hours each week at a given hourly wage. These workers are therefore classified as hourly 6 In the Online Appendix that accompanies the paper we show a series of additional results. In particular, we show sample statistics for each individual year and report our sample weights. We also show our key results without imposing sample weights. Finally, we show that ADP is truly a national firm in that it has a very representative geographic coverage. 9

11 Table 2: Statistics for Employee Sample, Selected Years All Number of Workers 1,000, , , ,991 Number of Firms 89,350 89,350 89,350 89,350 Number of Observations 22,642,878 1,319,797 2,744,414 2,778,947 Age (%) Age (%) Age (%) Age (%) % Male Average Tenure % Paid Weekly % Paid Bi-Weekly/Semi-Monthly % Paid Monthly % Hourly wage workers. However, on many levels, these workers operate as if they were salaried: their actual hours are never recorded and their hourly contract wage is just their weekly salary divided by 40. Furthermore, these workers may report being salaried in survey data such as the CPS. For our purposes, however, we consider these workers as hourly, matching the ADP-provided definition. Additionally, with respect to wage changes, all changes in perperiod earnings will be associated with a change in the hourly wage given that from the payroll system s perspective hours are fixed at 40 hours per week. Despite these differences in classification, the fraction reporting being paid hourly in the ADP data is similar to the CPS averages. Given that ADP is growing over time, so too is our sample. Of our 1 million workers, only 202,000 are in our sample in 2008 while 343,000 are in our sample in Despite the growing sample size over time as ADP expands its business, the demographic composition of workers is essentially constant over time. One distinction is that average tenure is falling over time. Given that the Great Recession occurred early in our sample, it is not surprising that average tenure fell as many workers became displaced during the recession. 10

12 2.3 Measuring Nominal Wage Adjustments The focus of this paper is on the frequency and size of wage changes. We consider changes in the worker s per-period payment rate as our measure of changes in the worker s nominal wage. To reiterate, our nominal wage measure is the hourly wage for hourly workers and per-period earnings for salaried workers. We aggregate our unit of observation to the month. Specifically, our nominal wage measures are defined as the wage paid to the individual during the last pay period of the month. Throughout the paper, we explore one-month, three-month (one-quarter) and twelve-month (annual) wage changes. Given that our nominal wage measures come from administrative HR records, there should be little, if any, measurement error in our wage measures. Despite this, there are some exceptionally small wage changes in our data resulting from salaried individuals earning annual amounts that do not easily divide into twelve months. As a result, we consider only wage changes of at least 0.1%. That is, if worker i earns wage w it in period t, we consider the object wit k = log w it log w it k for some k, and say that an individual has experienced a wage change in the previous k months if wit k > Figure 1 compares the average hourly wages for hourly workers in our ADP sample to average hourly wages in a similarly defined sample of year olds in the CPS. To get the hourly wage in the CPS, we use data from the outgoing rotation of respondents from the CPS monthly surveys. In the outgoing rotation, workers are asked if they are paid hourly and if so their hourly wage. For hourly workers, hourly wages are slightly higher in the ADP sample than in the CPS. This may be the result of the fact that, as discussed above, some salaried workers are classified as being hourly within the ADP data. Additionally, the ADP dataset does not include workers at small firms who are, on average, paid slightly less than workers at larger firms. The differences, however, between the ADP sample and the CPS sample are small and the trends are very similar suggesting that the ADP data is roughly representative of the entire U.S. population. Finally, for our analysis, we will separately analyze nominal wage adjustments for a sample of job-stayers as well as a separate sample of job-changers. Job-stayers are workers who remain employed at the same firm between the periods of t and t + k. Jobchangers are workers who move from one ADP firm to a new ADP firm between the periods of t and t + k. For our job-changer sample, workers could have another job or be nonemployed at some point between t and t + k. Given that we only measure job transitions from one ADP firm to another ADP firm, we cannot distinguish jobs at non-adp firms separately from being non-employment. Finally, when measuring nominal wage changes for job-changers, we only focus on workers who transition from either hourly-to-hourly jobs or from salaried-to-salaried jobs. 11

13 Figure 1: Hourly Wage Comparison ADP vs. CPS, Average Demographically Adjusted Nominal Wage CPS Hourly Wage ADP Hourly Wage Note: Figure shows the average hourly wage for hourly workers in our ADP sample and in a similarly defined sample of CPS respondents. Specifically, the CPS sample is restricted to workers between the ages of 21 and 60 who are paid hourly. For the average hourly wage for workers paid hourly in the CPS, we use data from the monthly outgoing rotation files from the CPS. In the outgoing rotation files, workers paid hourly are asked to report their hourly wage. The ADP data is weighted so it is representative of the aggregate industry size distribution. The CPS data is weighted by the corresponding survey weights for the respective samples. 12

14 3 The Allocation of Worker Compensation As discussed above, the primary focus of our paper is using a worker s per-period contract rate to measure the flexibility of a worker s wage over time. However, workers receive other forms of compensation including overtime payments, tips, commissions, and annual bonuses. In this section, we discuss how important these other margins are in terms of worker compensation. As we discuss below, the median worker receives 96.2 percent of her compensation from the per-period contract rates. However, for some workers annual bonuses are important. For another set of workers, a large part of their compensation comes from tips and commissions. The ADP dataset is one of the few datasets of which we are aware that allows researchers to measure the composition of worker compensation. Specifically, in addition to measuring a worker s per-period contract rate without error, the ADP data also include administrative measures of a worker s monthly gross labor compensation (excluding benefits). The monthly gross labor compensation measure is the sum of the worker s actual gross take home pay accrued during the month. We refer to all monthly earnings stemming from a workers per-period contract wage adjusted for either hours worked or the number of pay periods during a given month as being the worker s monthly base compensation. For hourly workers, base compensation would be the product of their perperiod hourly wage and the number of hours they worked during the month. Meanwhile, salaried workers who are paid weekly will have their monthly compensation be four or five times higher than their per-period weekly contract rate. However, workers also receive compensation during a month above and beyond their base compensation as measured by their per-period contract rate. Some workers work overtime and receive additional overtime compensation (e.g., time-and-a-half). Other workers receive part of their compensation in the forms of tips and commissions, or after meeting contractually stipulated production or sales targets. Some workers receive meal and travel reimbursements within their paychecks accrued during a given month. Finally, workers on occasion receive bonuses from their firms which show up in their take-home pay. 7 ADP firms are required to report a worker s per-period contract wage, the worker s hours worked (if they are hourly), and the worker s gross wage earnings (which shows up as a worker s gross (pre-tax) take home pay). However, the fact that firms are not required to provide detailed information on these other forms of compensation makes it difficult to ascertain with certainty the amount and composition of overtime, tips and commission, and bonus compensation. However, given the available information, we can make substantive progress on distinguishing both the size and composition of other forms of compensation. 7 Meal reimbursements also show up in workers monthly take-home pay. 13

15 In particular, for both hourly and salaried workers, we can create a measure of monthly residual earnings by subtracting monthly base compensation from actual gross monthly earnings. 8 These residual earnings will include meal and travel reimbursements, signing bonuses, severance pay, cash outs of unused vacation pay, overtime payments, commissions, tips, advance payments of paychecks, and bonuses accruing to the worker during a given month. One additional component of these residual earnings could be measurement error if the per-period contract rate changed during the month. Given we only have monthly aggregates and our monthly per-period contract rate is measured at the end of the month, any change in the wage during the month can cause a deviation between gross earnings and the per-period contract rate. To help assess how important other forms of compensation above and beyond their base earnings is to the workers total annual compensation, we temporarily restrict our sample to only those workers who remain continuously with the same employer for a full calendar year. For this set of workers, we compute a measure of their gross annual earnings by summing together their monthly gross earnings across all calendar months. Additionally, we compute a measure of their gross annual base pay by summing together their monthly base pay earnings across all calendar months. By taking the ratio of the two, we can create a measure of the share of all annual gross earnings that comes from their base pay. If the ratio equals 1, the worker during the year only receives base pay. When the ratio is less than 1, the worker is compensated with some additional residual payments throughout the year. Table 3 displays the distribution of the share of earnings accruing from base pay for our full sample (column 1) and our full-year sample (columns 2 and 3). Again, the full year sample is the sample of individuals who remain continuously employed with the same firm during a 12 month calendar year. We show patterns using monthly data (share of gross earnings during the month coming from base pay) and annual data (share of gross earnings during the year coming from base pay). The table shows that for most worker-month pairs, most earnings come from base pay. For example, even the 25th percentile of worker-month pairs has roughly 94 percent of earnings coming from base pay. However, for some workermonth pairs (around the 10 percentile), a substantial part of worker gross-monthly earnings comes from sources other than base pay. Again, this could stem from commissions, tips, overtime payments, signing bonuses, annual bonuses, meal and travel reimbursements, etc. The final column of the table shows the share of annual earnings coming from base pay. For the median worker during the period, roughly 96 percent of all earnings comes from base pay. Even the 25th percentile of worker-year pairs has workers receiving over 90 percent of all gross earnings coming from base pay. It is this reason that we chose to focus 8 See the Data Appendix for exact details on this procedure. 14

16 on base pay as our primary measure of worker compensation. Our nominal wage measure is directly related to base pay compensation. While workers receive many additional types of compensation above and beyond base pay compensation, one explicit type of compensation we wish to explore more fully is bonus pay compensation. Again, bonuses are not consistently measured within the ADP data. However, we can create a proxy for bonuses by using our residual income measure. To do so, we define a worker bonus as occurring if residual income exceeds one-percent of annual earnings in either December, January, February or March. Most firms pay annual bonuses in December (as a Christmas bonus ) or early in next calendar year. 9 We exclude small residual income payments in these months (less than 1 percent of annual earnings) from our bonus measure so as to exclude small deviations between monthly earnings and monthly base pay due to things like small measurement due to within changes in the workers contracted pay amount. Table 4 displays summary statistics for our broad bonus measure (top panel) summed over the period. Again, we use our sample of workers who remain continuously employed with the same employer during a full 12 month calendar year. Give our broad bonus definition, roughly one-quarter of all workers (column 1), one-fifth of all hourly workers (column 2) and one-third of all salaried workers (column 3) receive an annual bonus. The mean and median size of the bonus, conditional on a bonus occurring, is roughly 5 percent and 3.4 percent, respectively, of annual gross earnings. Not surprisingly, the conditional bonus share is higher for salaried workers than for hourly workers. The fact that the mean bonus share is larger than the median suggest that some workers are receiving really large bonuses during the month. Bonuses explain one important reason why a worker s annual gross pay exceeds their annual base pay. Our broad bonus measure is likely an upper bound on true bonuses given that it our measure of residual earnings in these four months are still potentially contaminated with some overtime, commission an tip payments earned in those months. For example, workers who are paid with commissions will have potentially residual payments in many months during the year. To potentially account for this, we exclude from our broad bonus measure any worker who has residual monthly earnings greater than 1 percent of their annual earnings in 3 or more months during the year. These are people who persistently have large residual earnings throughout many months of the year. We refer to this as our narrow bonus measure. The bottom panel of Table 4 shows that roughly 16 percent of all workers receive large residual payments in December-March but receive no large residual payments in other months of the 9 Over 85 percent of residual earnings (value weighted) accrued in these four months with the frequencies being by far the largest in December followed next by March. 15

17 Table 3: Share of Annual Compensation in Base Pay Sample All Full-Year Monthly Monthly Annual Data Data Data All Workers 10 th Percentile Share in Base 78.6% 78.3% 80.3% 25 th Percentile Share in Base 93.7% 93.6% 90.1% Median Share in Base 100% 100% 96.2% 75 th Percentile Share in Base 100% 100% 99.4% 90 th Percentile Share in Base 100% 100% 100% Hourly Workers 10 th Percentile Share in Base 83.4% 83.8% 84.7% 25 th Percentile Share in Base 93.2% 93.2% 92.0% Median Share in Base 99.2% 98.9% 96.9% 75 th Percentile Share in Base 100% 100% 99.3% 90 th Percentile Share in Base 100% 100% 100% Salaried Workers 10 th Percentile Share in Base 65.2% 65.3% 74.1% 25 th Percentile Share in Base 95.6% 95.3% 86.6% Median Share in Base 100% 100% 94.6% 75 th Percentile Share in Base 100% 100% 99.5% 90 th Percentile Share in Base 100% 100% 100% Note: Table shows the distribution across households in the share of their total gross earnings that is base pay. Columns 1 and 2 focus on monthly shares while column 3 focuses on annual shares. Columns 1 uses our full employee sample. Columns 2 and 3 restrict our sample to only those individuals who remain employed with the same employer for a full calendar year. The top panel includes data for all workers regardless of pay type while the bottom two panels includes data for hourly and salaried workers separately. 16

18 Table 4: Annual Bonus Distribution All Hourly Salaried Broad Bonus Definition Fraction with Bonus in Year 26.8% 22.3% 33.5% Mean Share of Pay in Bonus 1.2% 0.7% 2.0% Mean Share of Pay in Bonus, Conditional > 0 4.8% 3.3% 6.3% Median Share of Pay in Bonus, Conditional > 0 3.4% 2.2% 4.9% Mean Size of Bonus, Conditional > 0 $3,489 $1,676 $5,392 Median Size of Bonus, Conditional > 0 $1,727 $815 $3,709 Narrow Bonus Definition Fraction with Bonus in Year 15.7% 13.3% 19.6% Mean Share of Pay in Bonus 0.7% 0.4% 1.2% Mean Share of Pay in Bonus, Conditional > 0 4.5% 3.2% 6.0% Median Share of Pay in Bonus, Conditional > 0 3.1% 2.1% 4.7% Mean Size of Bonus, Conditional > 0 $3,149 $1,577 $4,877 Median Size of Bonus, Conditional > 0 $1,507 $751 $3,226 Note: Table shows the distribution of bonuses as measured in our ADP employee sample. For this analysis, we restrict the sample to those employees who remain with the same firm for a full calendar year. We define bonuses as being positive when a worker has residual earnings in the months of December, January, February and March. See text for definition of residual earnings. Our broad measure of bonuses (top panel) defines bonuses as any positive residual earnings accruing in December, January, February or March. Our narrow measure of bonuses (bottom panel) only includes individuals who positive residual earnings in one calendar month during December, January, February or March. 17

19 year. Again, bonuses are more common for salaried workers relative to hourly workers. Our narrow bonus measure is likely a lower bound on true annual bonuses received given that some of the commission workers that we may have excluded likely also receive a large annual end of the year bonus. Despite the potential measurement error concerns, we still think it valuable to explore the extent to which bonuses may vary over time for a given worker and how that variation evolves over the business cycle. So, in addition to just measuring nominal wage adjustments for a given worker (which comprises the overwhelming majority of their annual earnings for most workers), we are also going to explore bonus variation over time. Collectively, we think bonus pay and base pay comprise the two most important levers that firms can adjust with respect to the compensation of their workers Nominal Wage Adjustments for Job-Stayers In this section we present key facts about the nature of on-the-job wage adjustment. First, we measure the frequency and size of nominal wage adjustments for job-stayers, finding a strong asymmetry in wage changes on-the-job. We then explore whether nominal wage adjustments differ by firm size and industry. Finally, we highlight the importance of time dependence in wage setting at both the individual worker and firm level for job-stayers, and the extent to which bonuses provide a relevant margin of adjustment of workers compensation. 4.1 Main Results Figure 2 highlights the first key set of facts of the paper. The figure plots the distribution of 12-month wage changes for job stayers. As discussed above, our measure of the worker s nominal wage is their per-period contract rate. Panel A plots the distribution for hourly workers, while Panel B plots the distribution for salaried workers. Three key observations are apparent from the figure. First, a large share of workers - 33% of hourly, and 35% of salaried do not receive a nominal wage change in a given year. Second, there is a clear asymmetry in the wage change distribution, with the overwhelming majority of changes being wage increases. Of the roughly 66% of all individuals who receive a wage change over a given 12-month period, only 3.6% received a wage cut (2.4/66). Finally, there are very few small wage changes for either hourly or salaried workers. Just 8.6% of workers receive a wage change of between 0.1 and 2 percentage points, compared with 27.1% receiving between 2 10 Ideally, we would like to also explore fringe benefits. The ADP data needs more processing before such a similar systematic analysis of fringe benefits can be conducted. We hope to explore such an analysis in future work. 18

20 and 4 percentage points. This missing mass of very small wage changes is consistent with the random menu cost models that are so prevalent in the price setting literature. Figure 2: Nominal Wage Change Distribution for Job Stayers Percent Wage Change (%, 12-month) Percent Wage Change (%, 12-month) Panel A: Hourly Workers Panel B: Salaried Workers Note: Figure shows the annual change in nominal wages for workers in our employee sample who remain employed on the same job. We use our employee sample for this analysis. Table 6 provides a set of moments on the probability of wage increases and wage declines for three frequencies: monthly, quarterly and annual. The annual frequencies correspond to the underlying data shown in Figure 2. The first column pools together hourly and salaried workers while the second and third columns, respectively, show the frequency of wage changes for hourly and salaried workers separately. A few things are of note from the table. First, the frequency of wage changes is roughly similar between salaried and hourly workers. Roughly two-thirds of both receive annual wage changes over the entire sample period (summing over wage increases and wage declines). Second, while the average probability of a wage change is similar between the two groups in our sample of job stayers, salaried workers are more likely to receive a nominal wage cut. Over the entire sample, only 1.8% of hourly workers receive a nominal wage cut over a 12 month period while 3.6 percent of salaried workers receive a nominal wage cut. Third, one cannot simply extrapolate monthly nominal wage changes to quarterly or quarterly wage changes to annual. The probability of a quarterly nominal wage change is less than three times the monthly wage change and the probability of an annual nominal wage change is less than four times the quarterly change. This is likely due in part to well-known time aggregation issues arising from workers who receive multiple wage changes, as well as to the fact that the samples differ between the three horizons: for monthly wage changes, workers need to only remain with their employer for one month, while for annual wage changes workers need to remain with their employer for the full year. 19

21 Table 5: Probability of Wage Change, Pooled Sample of Job Stayers Monthly Quarterly Annual All Workers Probability of Positive Wage Change (%) Probability of Negative Wage Change (%) Hourly Workers Probability of Positive Wage Change (%) Probability of Negative Wage Change (%) Salaried Workers Probability of Positive Wage Change (%) Probability of Negative Wage Change (%) Note: Table shows the frequency of wage increases and wage decreases at different horizons for our sample of job-stayers during the period. The top panel pools together hourly and salaried workers while the middle and bottom panels, respectively, show the frequency of changes for hourly and salaried workers separately. The first column shows results at the monthly horizon while the second and third columns show results at the quarterly and annual horizons. We use our employee sample for this analysis. Table 5 shows additional moments of the wage change distribution. For this table, we pool together both hourly and salaried workers. 11 During this period, mean and median nominal wage growth for workers who remain on the same job equaled 3.9 percent and 2.4 percent, respectively. 12 Conditional on a wage change occurring, annual mean and median nominal wage growth was 5.6 and 3.2 percent. A key statistic we will focus on throughout the paper is the standard deviation of nominal wage growth. Unconditionally and conditional on a wage change occurring, the standard deviation of annual nominal wage growth during the full period was 6.5 percent and 6.9 percent, respectively. Consistent with the patterns in Figure 2, annual wage changes display very large amounts of both skewness and kurtosis. Conditional on a positive wage change occurring during a 12 month period, the mean and median size of the increase was 6.3 and 3.5 percent. The fact that the mean is much higher than the median reinforces the fact that some workers receive very large nominal wage changes, perhaps due to promotions. The mean and median size of a wage cut, conditional on the worker experiencing a nominal wage reduction were both around 7 11 The results were again roughly similar between hourly and salaried workers. 12 To limit the effect of extreme outliers when computing mean wage changes, we winsorize both the top and bottom 1% of nominal wages and the top and bottom 1% of wage changes. We only do this when computing the size of wage changes conditional on a wage change occurring. This does not affect our frequency of wage change results in any way. 20

22 percent. While the frequency of wage increases is much higher than wage cuts, the mean size of a wage increase conditional on it happening is nearly identical to the mean size of a wage cut conditional on it happening. The evidence presented in this section yield multiple lessons of importance for modelers and policymakers. First, we observe a large asymmetry in realized wage flexibility, with wages seemingly much more difficult to cut than raise. Although excessive downward nominal rigidities have been documented before in the literature (see, e.g. Lebow et al. (2003); Kahn (1997); Card and Hyslop (1997)), the presence of measurement error in hours and earnings in prior work has yielded quantitatively different magnitudes of this asymmetry. In addition, the missing mass of small wage changes urges consideration of models of state dependent wage adjustment, which we explore in more depth in Section 6. Again, this missing mass has been difficult to detect in prior work, for reasons explored in great detail in Section Nominal Wage Adjustments for Job-Stayers by Firm Size and Industry Figure 3 shows the distribution of annual wage changes over the period by firm size and industry. The top panel shows patterns for hourly workers while the bottom patterns for salaried workers. The figure shows that wage changes are monotonically increasing in firm size for both hourly and salaried workers. In a given 12-month period, 63.4% of hourly workers and 66.5% of salaried workers in firms with under 500 employees receive a wage change. The comparable numbers for firms with employees are 78.9% and 76.8%, respectively. These results complement the finding in the literature documenting that workers receive higher wages in larger firms (Brown and Medoff, 1989). Not only are workers in large firms receiving higher wages they also have a higher frequency of nominal wage adjustments. All of the variation across firm size groups is in the propensity to receive a nominal wage increase. While nominal wage cuts are rare for all workers, there is no systematic variation in the propensity of a nominal wage cut with firm size. Figure 3 also shows that there is a fair degree of heterogeneity across industries with respect to wage changes. For example, both hourly and salaried workers in the manufacturing industry are much more likely to receive a wage change than workers in construction during our sample period. Given that firms within different industries also differ by size, a natural question is how much of the variation across industries is due to differences is firm size. To assess this, we regressed the probability of a nominal wage change during a given year on a vector of firm size dummies and a vector of industry dummies. We also included a vector of additional controls including a quadratic in worker age, a quadratic in worker tenure, an indicator of whether the 21

23 Table 6: Wage Change Statistics, Pooled Sample of Job Stayers Monthly Quarterly Annual Unconditional Mean Wage Change (%) Median Wage Change (%) Standard Deviation of Wage Change (%) Skewness of Wage Changes (%) Kurtosis of Wage Changes (%) Conditional on Any Wage Change Mean Wage Change (%) Median Wage Change (%) Standard Deviation of Wage Change (%) Skewness of Wage Changes (%) Kurtosis of Wage Changes (%) Conditional on Positive Wage Change Mean Wage Change (%) Median Wage Change (%) Standard Deviation of Wage Change (%) Conditional on Negative Wage Change Mean Wage Change (%) Median Wage Change (%) Standard Deviation of Wage Change (%) Note: Table shows moments of the wage change distribution for different horizons for a sample of job-stayers in the ADP data between 2008 and For this table, we use our employee sample and pool together hourly and salaried workers. All data are weighted to be nationally representative of sample of workers working in firms with more than 50 employees. 22

24 Share with Wage Change over Prior 12 Months Share with Wage Change over Prior 12 Months Share with Wage Change over Prior 12 Months Share with Wage Change over Prior 12 Months Figure 3: Share with Wage Change by Firm Size and Industry, All Years 85% 80% 75% 70% 65% 63.4% 67.9% 72.0% 78.9% 80% 75% 70% 65% 64.1% 64.7% 65.2% 67.3% 71.0% 75.1% 75.6% 60% 55% 60% 55% 55.4% 50% 45% 40% Firm Size: Number of Employees 50% 45% Panel A: Hourly Workers by Size Panel B: Hourly Workers by Industry 85% 80% 75% 70% 65% 66.5% 72.9% 76.3% 76.8% 75% 70% 65% 60% 64.2% 65.4% 66.1% 69.9% 72.8% 60% 55% 50% 55% 50% 50.8% 54.2% 55.2% 45% 40% Firm Size: Number of Employees 45% Panel C: Salaried Workers by Size Panel D: Salaried Workers by Industry Note: Figure shows the probability of receiving a wage change by firm size and industry for a sample of job-stayers in the ADP data between 2008 and For this figure, we use our employee sample, and separately plot the patterns for hourly workers (Panels A and B) and salaried workers (Panels C and D). All data are weighted to be nationally representative of sample of workers working in firms with more than 50 employees. 23

25 worker is paid hourly, and a vector of state of residence month-year fixed effects. We also ran a version of the regression replacing the dependent variable with either the probability of a nominal wage increase during the year or the probability of a nominal wage cut during the year. The full results of these regressions are shown in the Online Appendix accompanying the paper. The results of the regression still show that there is a large and statistically significant gradient between firm size and the propensity of a nominal wage change. Workers in firms with over 5,000 employees are 10 percentage points more likely to experience a nominal wage change than workers in firms with employees. Likewise, workers in the manufacturing sector were 7 percentage points more likely to receive a nominal wage change relative to workers in the construction or retail trade industries, conditional on observables. 4.3 Time Dependence in Nominal Wage Adjustments, Job-Stayers Many modern macro models assume some time dependence in wage setting. For example, Taylor (1979, 1980) emphasizes that staggered wage contracts can amplify business cycle persistence in response to aggregate shocks. New Keynesian macro models in the spirit of Christiano et al. (2005) use acalvo (1983) model of wage setting. In this sub-section, we use our detailed micro data to explore evidence of time dependence in wage adjustment for our sample of job-stayers. The purpose of doing so is two-fold. First, this section provides some background summary statistics on the frequency and nature of wage adjustment for job-stayers. Second, the presence of time dependence in wage setting informs the models of wage setting that should be considered in labor and macroeconomics going forwards. Figure 4 plots the average number of wage changes during a given year for workers in our employee sample. As seen from Table 5, roughly 35 percent of job-stayers receive no wage change during a 12 month period. Over 50 percent of both hourly and salaried workers receive exactly one wage change during a 12 month period where they remained continuously on the job. Between 10 and 15 percent of job-stayers receive multiple wage changes during a given year. The take away from Figure 4 is that roughly 90 percent of job-stayers receive either zero or one nominal wage change during a given year. Multiple nominal wage changes within a year are rare for continuing employees who remain on the same job. To begin formally studying time dependence in wage setting, we exploit the individual level micro data and estimate an individual duration model of wage changes. Figure 5 plots the resulting hazard functions of wage adjustment for the subset of job-staying employees who experience at least two wage changes over our sample period. Specifically, the figure shows the probability of a one month wage change between t 1 and t conditional on the worker surviving to month t without a wage change at the same firm. 24

26 Figure 4: Number of Nominal Wage Changes over 12 month period, Job-Stayer Sample Percent Number of Wage Changes within Year Percent Number of Wage Changes within Year Panel A: Hourly Workers Panel B: Salaried Workers Note: Table shows the average number of nominal wage changes for hourly workers (left panel) and salaried workers (right panel). We use our employee sample for this analysis and restrict our sample to those workers who remain continuously employed with the same firm during a 12 month calendar year. We use all data between 2008 and 2012 and average over the calendar years. Figure 5: Hazard Function of Wage Change, Job-Stayers Panel A: Hourly Workers Panel B: Salaried Workers Note: Figure shows the hazard rate of a wage change between t 1 and t conditional on surviving to t without a wage change at the same firm. Sample only includes individuals with at least two wage changes. We use all data between 2008 and 2016 for this analysis, and weight the data to be representative of the firm size industry mix in the BDS. 25

27 The figure rejects the Calvo prediction that the probability of wage change is constant over time at the individual level for job-stayers. In most months, the probability of a wage change is roughly constant at about 3-4%. However, roughly 12 months after the last wage increase, individuals are much more likely to get another wage increase. Conditional on making it to month 11 with no wage change, there is over a 50% probability than an individual gets a wage increase in month 12. Note, given a little bit of calendar variation, there are small spikes at 11 and 13 months as well. We also see another spike in the hazard at 24 months and a more modest spike at 36 months. Moving away from a hazard analysis, we can define a sample of individuals who remained on their job for the next 18 months after a prior wage change. We can then ask how many of these workers got their next wage change months later. Of consistently employed workers, 30% receive their next wage change exactly one year after their prior wage change. Figure 5 provides some evidence of time dependence in wage adjustment. The majority of wage changes occur annually. However, basic models of purely time dependent wage setting have predictions regarding the average size of wage changes. Under standard productivity processes with positive drift, individuals who are able to renegotiate their wage every month would negotiate smaller increases in their wages than those who renegotiate only once per year, on average. As a result, those who wait longer between wage changes should observe larger average changes in absolute value. We explore this prediction next. Figure 6 shows the average size of the wage change for job stayers by the time since last wage change. Since the vast majority of wage changes for job stayers are positive, this figure only includes workers who received a positive wage change. While most wage changes occur at 12 month frequencies, Figure 6 shows that the size of the wage changes at these annual frequencies are much smaller than wage changes that occur at other times of the year. These predictions are not consistent with a standard Calvo (or Taylor) model at the individual level. However, the patterns could be consistent with a broader model of selection. If the workers who get these wage changes that occur off-cycle are positively selected in some way, this could explain why they receive higher wage increases. For example, if the worker receives an outside offer, the firm may have to raise the worker s wage earlier than their annual cycle in order to retain the worker. Or, if a worker is promoted internally and the promotions are distributed throughout the year, it is not surprising that workers who receive a wage change off cycle also get larger wage changes. Figure 7 shows the time dependence in wage setting at the firm level. For this analysis, we use our sample of 3,000 unique firms. We restrict the firm level sample to only include firms who remain in the sample of all 12 months during a given calendar year. Then, for each firm-year pair, we compute the fraction of workers who received a nominal wage change 26

28 Figure 6: Mean Size of Wage Changes by Time Since Last Change, Job-Stayers Panel A: Hourly Workers Panel B: Salaried Workers Note: Figure shows the mean size of wage increases for workers receiving a wage increase t months after their last wage change. Sample only includes individuals with at least two wage changes. Additionally, we restrict our analysis to the job-stayer sample. during each calendar month. We then rank the months within a given firm-year pair from the month with the highest fraction of nominal wage changes to the month with the lowest fraction of nominal wage changes. For example, for some firms the highest month may be September while for other firms the highest month may be January. We then take the simple average probability of a worker receiving a wage change across firm-year pairs for each ranked month. 13 The figure shows that when a firm tends to adjust wages, it makes all their wage adjustments during one particular month of a given year. For example, a typical firm adjusts 50 percent of their workers wages in the month where they make the most wage changes. Given that only about 65 percent of workers get a wage change (in the population as a whole) and the fact that we are averaging over firms and not workers, the figure suggest that firms do most of their wage changes in one month out of the year. 14 As a point of contrast, firms only adjust roughly 10 percent of their workers wages in the second highest ranked month. The fact that the share of wages adjusted are roughly flat between the second highest ranked month and the 12 highest ranked month is consistent with the worker data where some adjustments are occurring off-cycle at a roughly constant hazard. These changes are likely 13 We also restrict our sample to only firm-year pairs where the firm adjusted at least 25 percent of their workers wages at some point during the calendar year. We do this to focus on firms who are adjusting wages to avoid a problem with firms no wages during the year. This restriction is not too binding as 91% of firm-year pairs in our sample adjusted at least 25 percent of their workers wages during the year. 14 This observation represents the labor market analogy to the price-setting rule employed in Midrigan (2011) in which multi-product firms enjoy economies of scale in coordinated output price adjustment. 27